Problem: Simplify the following expression: $q = \dfrac{p^2 + 7p - 8}{p + 8} $
Answer: First factor the polynomial in the numerator. $ p^2 + 7p - 8 = (p + 8)(p - 1) $ So we can rewrite the expression as: $q = \dfrac{(p + 8)(p - 1)}{p + 8} $ We can divide the numerator and denominator by $(p + 8)$ on condition that $p \neq -8$ Therefore $q = p - 1; p \neq -8$